Metal Magnetohydrodynamic Research Articles

Proposal of novel exergy-based sustainability indices and case study for a biomass gasification combine cycle integrated with liquid metal magnetohydrodynamics

Exergy is considered a way to sustainability. Exergy-based analyses have been recently widely used for performance assessment and comparison purposes of energy systems from production to end-user while different sustainability related indices or indicators including exergetic concepts have been developed in the literature. In this regard, the present study proposed five different indices: (i) Exergetic Fuel Based Environmental Remediation Index (χ), (ii) Exergetic Product Based Environmental Remediation Index (δ), (iii) Exergetic Fuel Based Total Environmental Remediation Index (β), (iv) Exergetic Product Based Total Environmental Remediation Index (α), and (v) Improved Sustainability Index (ISI). These indices were applied to a novel Biomass-integrated Gasification Combine Cycle (BIGCC) integrated with Liquid Metal Magnetohydrodynamics (LMMHD). They allowed to perform a more complete environmental analysis by considering the exergetic cost of environmental remediation of the process. The average exergy efficiency values for the BIGCC, LMMHD and the overall system were determined as 0.491, 0.222 and 0.688 under daily ambient temperatures for a year and different air to fuel ratio (AFR) conditions, respectively. The average values for χ, β, δ, α and ISI were 1.636, 2.389, 1.949, 2.848 and 0.513, respectively.

Validation and verification of a quasi two-dimensional turbulence model and an eddy detection method for liquid metal magnetohydrodynamics flows

The flow of liquid metals in straight rectangular channels with an externally applied transverse magnetic field is considered for breeding blankets in tokamak fusion reactors. Under the tokamak magnetic field, the liquid metal experiences the magnetohydrodynamic (MHD) effect that enhances the laminarization of the flow. In geometric singularities, or under certain flow conditions, the combination of Lorentz forces, momentum, and buoyant forces may trigger the formation of vortical structures. The generated vortices will align with the direction of the magnetic field, and therefore the use of a quasi-two-dimensional (Q2D) model is convenient to study them assuming that the walls are electrically insulating and the Hartmann number is high enough. Using this model is computationally affordable, allowing extensive parametric analyses. To identify the presence of eddies in the two-dimensional domain, the application of the bi-dimensional fast Fourier transform (FFT2) is foreseen as an adequate detection method. This work presents a methodology to systematically calculate liquid metal MHD flows with a Q2D model and evaluate the formation of eddies in the flow domain. The work includes a description of the validation and verification of the Q2D MHD model and of the FFT2 method proposed to automatically identify eddies. The sensitivity of the detection method is analyzed to subsequently apply it in parametric analyses.

Stabilized FEM solution of MHD duct flow with conducting cracks in the insulation

In this paper, the numerical solution of the fully developed liquid–metal magnetohydrodynamic (MHD) flow is given in a rectangular duct under an external oblique magnetic field with no-slip and insulated walls containing crack regions. The coupled MHD flow equations are transformed first into decoupled convection–diffusion equations in terms of the velocity and induced magnetic field. Thus, we apply the SUPG stabilization in the finite element method (FEM) solution procedure for high values of Hartmann number which determine the convection dominant case. Numerical solutions for high values of Hartmann number and several orientation angles of external magnetic field as well as different crack configurations depict the effects of these parameters on the flow, flowrate and induced current. The SUPG in the FEM solution of MHD equations enables one to display the well-known characteristics of MHD pipe flow for large values of Hartmann number in which wall insulation is faced to several cracks. It is found that, the flowrate drops with an increase in the Hartmann number, and the increase in the number and lengths of the cracks which are located on one Hartmann wall. The flowrate is minimum if the crack is located at the center of the Hartmann wall. If the crack is located on the side layer, it does not significantly affect the flowrate. The case of each Hartmann wall contains one crack, significantly drops the flowrate compared to two cracks on the same Hartmann wall. Also, the breakdowns and peaks are sharpened when the Hartmann wall is a curved boundary. The FEM with SUPG stabilization is capable of capturing flow changes for high values of Hartmann number even in the vicinity of small-sized crack regions.

Experimental and numerical investigation of gas-liquid metal two-phase flow pumping

Adapting an efficient method for pumping gas-liquid metal two-phase flow can make liquid metal magnetohydrodynamics (LMMHD) power generation systems economically feasible. An experimental facility was developed using a dual injection gas-lift pump to provide the circulation needed for the liquid metal in the LMMHD system. Also, a numerical simulation was performed in order to understand the behaviour of the two-phase flow through the gas-lift pump and be able to optimize the pump design for the best operational condition of the LMMHD system. In addition, the data were compared to a 1-D drift flux model that predicted the performance of the pump within the loop. The numerical results were found to be in an agreement with the experiments within ±25% which is considered adequate for optimization and design purposes of a two-phase flow system. The dual injection design was evaluated, and the axial injection mode was found to be more efficient in providing the required pumping than radial mode. Moreover, the flow visualization of the two-phase flow patterns seen in the pump riser was captured both experimentally and numerically indicating a swirl-like motion that can potentially be used to enhance heat transfer in the actual operational setting. Also, the optimum condition for pumping was found to occur at a slug-like flow structure in the riser.

Laboratory Characterization of a Liquid Metal MHD Generator for Ocean Wave Energy Conversion

Harnessing ocean wave energy is an old challenge that has gained momentum in recent years. In this paper, we present the flow and electrical characterization of a prototype of an alternate liquid metal magnetohydrodynamic (MHD) generator at a laboratory scale which has the potential to make use of the energy of marine waves for its conversion into electrical energy. The eutectic alloy Galinstan, used as a working fluid, was driven in oscillatory motion in a duct of a rectangular cross-section exposed to a transverse magnetic field generated by permanent neodymium magnets. The electric current induced by the motion of the liquid metal in the magnetic field was collected through copper electrodes and delivered to the load. The oscillatory axial velocity component along the duct was measured using ultrasonic Doppler velocimetry for different oscillation frequencies. In turn, the output currents and voltages were measured for different operation conditions and the electric power and efficiency were estimated from experimental measurements. The coupling of this generator to a wave energy converter (WEC) is discussed.

Numerical Research on the Flow Fields in the Power Generation Channel of a Liquid Metal Magnetohydrodynamic System.

The flow fields in the power generation channel of a magnetohydrodynamic system, which uses a mixture of liquid metal as the power generation medium and a low-boiling-point working medium as the carrying medium, were numerically investigated in the present paper. The influences of the magnetic field intensity, void fraction, and bubble diameter were examined, respectively. The results indicate that an increase in the magnetic field intensity will enhance the turbulence intensity and may reduce the stability of the flow fields, whereas increasing the void fraction will contribute to better flow stability in the power generation channel. The effect of the bubble diameter on the flow field stability is negligible in the range of the study. In addition, it is found that the volume fraction of the gas phase exhibits an M-shape distribution by studying the variation of the slip velocity over time. This paper presents our latest findings and will provide a fundamental theory for future design and operation of liquid metal magnetohydrodynamic systems.

Liquid metal free surface dynamics in rotating permanent magnet stirrer

We study liquid metal stirring by rotating permanent magnets in a laboratory-scale rectangular glass container. The main goal is numerical model validation using experimental free surface shape data. We find reasonable agreement between the experiments and coupled liquid metal magnetohydrodynamics simulations. Since the surface tension forces are not dominant here, free surface is deformed mainly by the dynamic pressure of the bulk flow. Therefore, we can conclude that not only the free surface profile is similar to experiments, but the bulk flow must be also very similar.

Effect of static liquid Galinstan on common metals and non-metals at temperatures up to 200 °C

Liquid metal Galinstan (GaInSn) is corrosive in nature against other solid metals as its base component is gallium. This study experimentally investigated the compatibility of GaInSn with eight common metals at temperatures up to 200 °C for 2000 h, including aluminum, copper, brass, ferritic and austenitic stainless steels (E-brite, SS304L, SS316L), and nickel-chromium alloys (Inconel and Hastelloy). This assessment aims to assist in design and material selection of a liquid metal magnetohydrodynamics system that houses Galinstan for power generation by low temperature natural heat sources or industrial waste heat. Design and fabrication of this renewable power system required assurance of material compatibility with common construction and instrumentation materials. The most severe corrosion effects of GaInSn on the metal alloys were observed on aluminum, copper, and brass, which confirms the results of previously conducted studies. No obvious corrosion on stainless steel or nickel–chromium alloys were observed by this study, which reveals that stainless steel has a good resistance to attack by GaInSn up to 200 °C. Six non-metals were also evaluated, including acronitrile butadiene styrene (ABS), acrylic, nitrile rubber (Buna N), nylon, polyvinyl chloride (PVC), and Teflon, which were deemed to be compatible with GaInSn up to the temperatures tested.

Numerical Characterization of a Liquid Metal Magnetohydrodynamic Alternate Generator in the Laminar-Regime under Inductionless Approximation

Numerical Characterization of a Liquid Metal Magnetohydrodynamic Alternate Generator in the Laminar-Regime under Inductionless Approximation

Numerical modelling of liquid metal magnetohydrodynamic flow in an electrically and thermally coupled annulus under reduced gravity

For a high-precision spaceborne magnetohydrodynamic (MHD) sensor, temperature drift is troublesome for engineers. The thermal properties of liquid metal MHD (LMMHD) flow in the sensor should be considered. The thermo-fluid behaviour of LMMHD flows and its effect on the output characteristic of the sensor were numerically investigated to explore the underlying mechanism. Based on the Boussinesq approximation, a three-dimensional model of the MHD effect in an electrically and thermally coupled annulus was simplified and implemented in a finite-element framework. The visual patterns of the velocity and electric potential depended on the type of temperature boundary, the magnitude and direction of the applied force, and the angular rate of the inlet and outlet. When the magnitude of the applied force increased from microgravity to gravity, the fluid gradually transformed from a viscous flow to a convective flow. The competitive action between the magneto- and natural convection had a substantial influence on the distribution of the electric potential, as the applied force was perpendicular to the magnetic field. The result will provide a reference for space applications and ground tests of MHD sensors.

Investigations of liquid metal magnetohydrodynamic rectangular duct flows under inclined transversal magnetic fields

Numerical simulations on liquid metal magnetohydrodynamic (MHD) flows in rectangular ducts with conducting or insulating walls under uniform or gradient inclined transversal magnetic fields are conducted in this study. The results of the influence of the inclined angles of the external magnetic fields on the MHD flow state are obtained. Numerical simulations based on fully developed modeling are conducted to investigate the influence of the inclined uniform magnetic field. This is a two-dimensional (2D) full solution for MHD duct flows. Three-dimensional (3D) numerical simulations using a code based on Open Field Operation and Manipulation (OpenFoam) are performed. This is a full 3D solution based on the electrical potential equations. The results of the 3D simulations confirm the 2D numerical simulation results. The effects of the inclined gradient magnetic fields on the MHD duct flow state are also studied using 3D numerical simulations. The effects of the inclined fringing magnetic fields on MHD pressure gradients and velocity distributions are presented. Numerical results of the MHD pressure gradients under a fringing magnetic field with no inclination agree with the experimental results from ALEX. The velocity jets will be pulled from the two corners of the duct in the upstream to the other two corners of the duct in the downstream due to the 3D MHD effects caused by the fringing magnetic field.

Numerical simulation of two-fluid magnetohydrodynamic channel flows

A study of liquid metal magnetohydrodynamic (MHD) flows is important for analyzing flows in the Test Blanket Module of the proposed International Thermonuclear Experimental Reactor. Possible accident scenarios involve the leakage of coolant into the liquid metal flow. To address this situation, the present article considers the simplified case of two-dimensional isothermal flow of two fluids of different viscosities and electrical conductivities. We present analytical solutions to the fully developed flows and a solver based on OpenFOAM. We validate the solver performance with the analytical solution, and also the limiting cases of single fluid MHD flow and two-fluid hydrodynamic flow.

Performance Analysis of Heaving Float Wave Energy Converter with Liquid Metal MHD Generator

Heaving float wave energy converter/conversion (WEC), which makes use of liquid metal magnetohydrodynamics (LMMHD) generator, converts directly the linear motion of heaving float into electrical power. In this paper, effect of magnetic flux density on performance of heaving float LMMHD-WEC is analytically investigated. The results reveal that the capture width ratio, the load voltage, the output power, the system efficiency have maximum values with the increase of magnetic flux density.

Pressure distribution in MHD flows in an experimental test-section for a HCLL blanket

Liquid metal magnetohydrodynamic (MHD) flows in a scaled mock-up of a Helium cooled lead lithium blanket have been investigated experimentally in the MEKKA laboratory at the Karlsruhe Institute of Technology. The test section consists of 8 breeder units (BUs) connected two by two at the first wall (FW) through a series of small openings. The large boxes are fed and drained by poloidal manifolds formed by two parallel channels separated by a step-shaped wall, which is electrically conducting. The complexity of the geometry and the strong 3D MHD effects that characterize the flow in the mock-up are at the present time still very challenging for numerical simulations. Therefore, experiments are required to obtain an overview of pressure and velocity distributions in such geometry and to derive scaling laws to extrapolate the results to realistic ITER operating conditions. Pressure differences between several points on the test section have been measured. The influence of magnetic field strength and flow rate on pressure losses in the mock-up has been studied. The largest pressure drops occur along the manifolds. Another significant part of the entire pressure drop comes from flow near the FW, where the liquid metal passes through small gaps into the adjacent BU. This pressure drop between external pairs of BUs is at least 4–5 times larger than that in the internal ones. This suggests an inhomogeneous partitioning of the liquid metal flow among the BUs, which is related to the geometry of the manifold.

Validation of COMSOL code for analyzing liquid metal magnetohydrodynamic flow

Applicability of COMSOL multiphysics software for analyzing liquid metal MagnetoHydroDynamic (MHD) effect under fusion relevant parameters has been verified. For this purpose, few benchmark problems recommended by fusion MHD community have been simulated. The selected benchmark problems are steady state fully developed MHD duct flow, duct flow under transverse fringed magnetic field and transient phenomenon of natural convection in presence of magnetic field. Apart, from the recommended benchmark problems, an experimental scenario has been simulated having flow geometry with multiple 90° bends. For these simulations, two to three available independent physics modules have been suitably coupled under the single platform of COMSOL. The computed numerical results show good agreement with the available analytical or experimental or reported numerical data in the range of MHD parameters Hartmann number ∼104, Interaction parameter ∼104, wall conductance ratio ∼10−2 & Grasshof number ∼106.

Large eddy simulation of geometry sensitivity of magneotohydrodynamic turbulent flow in a rectangular duct

Velocity distributions and pressure drops in liquid metal magnetohydrodynamic (MHD) duct flows are closely associated with the shape of the duct cross-section. In order to investigate the effects of the cross-sectional shape on MHD turbulent flows, liquid metal flow in two kinds of rectangular duct with a uniform magnetic field applied transversely to the flow are simulated using large eddy simulation with the coherent structure model. One duct has a normal rectangular cross-section (N-duct), while the other rectangular duct has a triangular protrusion pointing into the flow domain at the middle of the walls parallel to the magnetic fields (P-duct). Both duct walls are electrically insulating, and the inlet and outlet of the computational domain are set to be periodic. The flow Reynolds number is kept constant in this study, while the Hartmann numbers vary from 10 to 42.4. The numerical results show that the protrusion at the parallel walls promotes flow turbulence and compensates the effect of turbulence suppression due to the magnetic field. As the Hartmann number increases, the turbulent MHD flow transits to a single-sided turbulent flow and finally to a laminar flow. The protrusion at the side wall promotes the turbulence and delays the MHD turbulent-laminar transition as the Hartmann number increases. However, the skin friction coefficient is higher in P-duct than that in N-duct when the flow is turbulent. The protrusion cannot reduce the pressure drop in rectangular duct with insulating walls.

Experimental investigations on liquid metal MHD turbulent flows through a circular pipe with a conductive wall

Experimental results on a liquid metal magnetohydrodynamic (MHD) turbulent flow through a circular conductive pipe subject to a uniform transversal magnetic field are summarized in this paper. The results of the MHD turbulent velocity distributions inside the conductive pipe are obtained. The velocity profiles along the center line of the middle cross section of the pipe are given. There are no big velocity jets in the Robert layers. The velocity distribution agrees well with the numerical simulation result. The transient turbulent velocity of one point in above mentioned line changing with times are measured in the experiment, it is found that the transient velocity varies dramatically compared to the average velocity at high Reynolds number (Re). The strong magnetic field suppresses the turbulent velocity fluctuation. The velocity profiles varying with the different Reynolds numbers at the same Hartmann number (Ha) are also presented in this paper. It is shown that the velocity in the center fluid area decreases with the Reynolds numbers increasing. The Reynolds stresses at different Reynolds numbers and Hartmann numbers are also derived from experimental data. The Reynolds stresses decrease with the increasing of Hartmann numbers. The map of laminar-turbulent transition for MHD circular conductive pipe flows at high Reynolds and Hartmann numbers are also presented. A different fluid instability from the theoretical prediction in Refs. Lielausis (1975) and Moresco et al. (2004) is observed and the transition condition is Re/Ha>20.

Influence of modifications of HCLL blanket design on MHD pressure losses

In 2008–2009 experiments have been performed to investigate liquid metal magnetohydrodynamic (MHD) flows in a scaled mock-up of a helium cooled lead lithium (HCLL) blanket. In order to improve the mechanical stiffness of HCLL blanket modules the design of the stiffening plate between two hydraulically connected breeder units (BUs) has been later modified. In the former design the liquid metal passed from one BU into the adjacent one by flowing through a narrow gap that extended along the entire width of the BU. In the most recent design this opening has been replaced by a series of smaller gaps. Therefore the velocity increases locally owing to the reduced cross-section along the flow path and the liquid metal contracts and expands along magnetic field lines to enter the neighboring BU. These flow conditions are known to create additional MHD pressure losses. In order to estimate the influence of design changes on MHD flow and pressure drop the previous test section has been adapted to the new design. Experimental results show that the modifications of the design at the first wall lead to an increase of pressure drop near the first wall by a factor 3–3.5. As a consequence the total pressure drop becomes larger. The 3D MHD phenomena that occur at the first wall seem to be mainly related to inertia effects that are confined in layers parallel to the magnetic field.

Experimental and numerical study of electrically driven magnetohydrodynamic flow in a modified cylindrical annulus. I. Base flow

Shear layers in confined liquid metal magnetohydrodynamic (MHD) flow play an important role in geo- and astrophysical bodies as well as in engineering applications. We present an experimental and numerical study of liquid metal MHD flow in a modified cylindrical annulus that is driven by an azimuthal Lorentz force resulting from a forced electric current under an imposed axial magnetic field. Hartmann and Reynolds numbers reach Mmax ≈ 2000 and Remax ≈ 1.3 × 104, respectively, in the steady regime. The peculiarity of our model geometry is the protruding inner disk electrode which gives rise to a free Shercliff layer at its edge. The flow of liquid GaInSn in the experimental device ZUCCHINI (ZUrich Cylindrical CHannel INstability Investigation) is probed with ultrasound Doppler velocimetry. We establish the base flow in ZUCCHINI and study the scaling of velocities and the free Shercliff layer in both experiment and finite element simulations. Experiment and numerics agree well on the mean azimuthal velocity uϕ(r) following the prediction of a large-M theoretical model. The large-M limit, which is equivalent to neglecting inertial effects, appears to be reached for M ≳ 30 in our study. In the numerics, we recover the theoretical scaling of the free Shercliff layer δS ∼ M−1/2 whereas δS appears to be largely independent of M in the experiment.

Investigation of Coupling MHD Rectangular Ducts Flows Based on a Fully Developed Modeling

Liquid metal magnetohydrodynamic (MHD) flows through the electrical coupling rectangular ducts are investigated based on a fully developed modeling. Numerical simulations of four different coupling MHD duct flows are carried out to get the results of the MHD pressure drop and the velocity distribution. The first and second cases are that the coupling rectangular ducts are arranged along the direction of external magnetic field, the flow direction in the two ducts is the same in case 1 but it is opposite in case 2; in the third and fourth cases, another coupling duct is extended along the perpendicular direction of the external magnetic field, the flow direction is identical in case 3, but it is opposite in case 4. Numerical results of the velocity and the induced electrical current distributions in the cross sections of the coupling ducts are given in those four different cases, it is indicated that the external magnetic field has a different effect on the flow pattern in those four cases. The MHD pressure drop in those four different cases is compared with the result of one normal rectangular duct flow, the MHD pressure drop of case 1 is reduced compare with the result of one normal duct MHD flows and result of case 4 is closed to one normal duct case, but the results of cases 2 and 3 are larger than it, especially for case 2 it is several times larger than the result of one normal duct flow. In addition, the MHD pressure gradients in those four cases decrease with the increase of the wall conductance ratios when the other conditions are the same. In the case, the three coupling duct flows when the flow direction of the middle duct is opposite, the strong magnetic field has very significant effect on the flow pattern in the middle coupling duct, and the MHD pressure gradient in the middle duct can be dozens of times bigger than that of one normal single duct flow. These results should be considered in the future liquid blanket design.